Related papers: The Navier-Stokes equations in $\mathbb R^2_+$ wit…
The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit: $\nu \to 0$. In \cite{Grenier}, one of the authors proved that there exists no asymptotic expansion involving one Prandtl's…
In this paper, we study the long-time behavior of the solutions to the two-dimensional incompressible free Navier Stokes equation (without forcing) with small viscosity $\nu$, when the initial data is close to stable monotone shear flows.…
We consider the problem of the stability of the Navier-Stokes equations in $\mathbb{T}\times \mathbb{R}_+$ near shear flows which are linearly unstable for the Euler equation. In \cite{greniernguyen}, the authors prove an $L^{\infty}$…
We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and…
Heuristic derivations of the Navier-Stokes equations are unable to reveal the applicability limits of these equations. In this paper we rederive the Navier-Stokes equations from kinetic theory, using a method that affords a step by step…
We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is…
In this paper, we study the Navier-Stokes equations of compressible, barotropic flow posed in a bounded set in $\mathbb{R}^3$ with different boundary conditions. Specifically, we prove that the local-in-time smooth solution of the…
This paper concerns the validity of the Prandtl boundary layer theory for steady, incompressible Navier-Stokes flows over a rotating disk. We prove that the Navier Stokes flows can be decomposed into Euler and Prandtl flows in the inviscid…
It is well known that the full compressible Navier-Stokes equations can be deduced via the Chapman-Enskog expansion from the Boltzmann equation as the first-order correction to the Euler equations with viscosity and heat-conductivity…
The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite…
We prove that the Navier-Stokes equation is well-posed in function spaces on $\mathbb{R}^d$, $d\ge 2$, that contain vector fields of order $O(|x|^\kappa)$ as $|x|\to\infty$ with $\kappa<1/2$. The corresponding solutions depend continuously…
In this paper, we prove in two dimensions global identifiability of the viscosity in an incompressible fluid by making boundary measurements. The main contribution of this work is to use more natural boundary measurements, the Cauchy…
The existence and uniqueness of the analytic solutions to the nonlinear Prandtl equations with Robin boundary condition on a half space are proved, based on an application of abstract Cauchy-Kowalewski theorem. These equations arise in the…
In this paper, we show the incompressible and vanishing vertical viscosity limits for the strong solutions to the isentropic compressible Navier-Stokes system with anistropic dissipation, in a domain with Dirichlet boundary conditions in…
We investigate the high viscosity limit (also called inertial limit) of the barotropic compressible Navier-Stokes equations supplemented with initial data which are perturbations of a stable constant solution. In the case of constant…
This paper is concerned with the evolution of two incompressible, immiscible fluids in two dimensions governed by the inhomogeneous Navier-Stokes equations. We prove global-in-time well-posedness, establishing the preservation of the…
We consider the three-dimensional incompressible Navier--Stokes equations in a curved thin domain with Navier's slip boundary conditions. The curved thin domain is defined as a region between two closed surfaces which are very close to each…
We are concerned with the inviscid limit of the Navier-Stokes equations on bounded regular domains in $\mathbb{R}^3$ with the kinematic and Navier boundary conditions. We first establish the existence and uniqueness of strong solutions in…
We consider the 2D, incompressible Navier-Stokes equations near the Couette flow, $\omega^{(NS)} = 1 + \epsilon \omega$, set on the channel $\mathbb{T} \times [-1, 1]$, supplemented with Navier boundary conditions on the perturbation,…
In this paper, we provide rigorous justification of the hydrostatic approximation and the derivation of primitive equations as the small aspect ratio limit of the incompressible three-dimensional Navier-Stokes equations in the anisotropic…